A Three-Stage Optional Randomized Response Model
In Gupta et al. (2010; 2011), it was observed that introduction of a truth element in an optional randomized response model can improve the efficiency of the mean estimator. However, a large value of the truth parameter (T) may be needed if the underlying question is highly sensitive. This can jeopardize respondent cooperation. In what we call a “three-stage optional randomized response model,” a known proportion (T) of the respondents is asked to tell the truth, another known proportion (F) of the respondents is asked to provide a scrambled response, and the remaining respondents are instructed to provide a response following the usual optional randomized response strategy where a respondent provides a truthful response (or a scrambled response) depending on whether he/she considers the question nonsensitive (or sensitive). This is done anonymously based on color-coded cards that the researcher cannot see. In this article we show that a three-stage model may turn out to be more efficient than the corresponding two-stage model, and with a smaller value of T. Greater respondent cooperation will be an added advantage of the three-stage model.
AMS Subject Classification62D05
Key-wordsQuantitative sensitive variable Randomized response Split sample Three-stage model
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- Gupta, S. N., S. Mehta, J. Shabbir, and B. K. Dass. 2012. Generalized scrambling in quantitative optional randomized response models. Commun. Stat. Theory Methods, (in press).Google Scholar